There are generally two types of light intensity optical modulators, electro-optic (EO) and electroabsorption modulators (EAM). The EO modulator is based on interferometry where the refractive index is controlled by applying an external field, usually implemented in form of a Mach-Zender Interferometer (MZI), disclosed in a textbook by Koichi Waikita with the title “Semiconductor optical modulators” published by Kluwer Academic Publisher in USA, 1998 which is hereby incorporated as a reference in its entirety. Electroabsorption modulators are usually based on band to band absorption controlled by an external field through the Frans-Keldych or quantum confined stark effect (QCSE).
The usual figure of merit (FOM) used for optical modulators includes weighting of device parameters as drive voltage (Vdrive), electrical bandwidth (3 dBe), and DC load impedance (ZL):
  FOM  =                    2        *                  Z          L                            50        +                  Z          L                      ⁢          f              3        ⁢        dBe              ⁢          λ              1.55        ⁢                                  ⁢        µm              ⁢          V      drive      Where Vdrive is the required voltage for a specified extinction ratio (ER), e.g. 10 dB or 20 dB for electroabsorption modulators, and Vπ for electro-optic modulators. The required ER should reflect the application the device is intended to be used in.
Electroabsorption modulators usually have a strong interaction between the electrical and the optical field and are therefore normally compact in size and show a low drive voltage. Therefore, the suggested FOM shows a clear advantage in favour for EAM. The compatible process for integration together with a laser, as well as the possibility to design with low polarization sensitivity can further motivate the use of an EAM. The electro-optic modulator does however show other advantages not included in this FOM such as well-defined non-linearity and controllable chirp.
Several EAM devices with an electrical bandwidth of more than 30 GHZ are presented in the Doctorial Dissertation by Robert Lewén, Royal Institute of Technology, Department of Microelectronics and Information Technology, Stockholm Sweden, publicly available 19 Jun. 2003, which is hereby incorporated as reference in its entirety.
In U.S. Pat. No. 6,160,654, by Kawano, an ultra high-speed semiconductor optical modulator with travelling wave electrode is disclosed, which has both advantages of a lumped-element electrode construction and a travelling wave electrode construction. A disadvantage with this construction is that the characteristic impedance of the electrical transmission line is relatively low, usually around 25Ω. Such low device impedance is usually not preferred within a standard microwave environment with a system impedance of 50Ω. Furthermore, this low impedance leads to a reduction of the suggested FOM (see above).
Another disadvantage with this construction is that the electrical and optical wave may propagate with different velocities. This effect will degrade the performance of the modulator.
Different approaches have been proposed to overcome the problems with low characteristic impedance and velocity matching. For electro-optical modulators one method, described in an article by R. G. Walker with the title “High-speed Semiconductor Intensity Modulators”, published in IEEE Journal of Quantum Electron., vol 27, no 3, pp 654-667, 1991, is to divide the continuous modulator into several shorter active elements, in which the optical propagation constant is set by an electrical field given by the voltage of an applied control signal. This approach was originally proposed by U. Langmann and D. Hoffmann in a presentation at the International Microwave Symposium, Dallas, 1982, with the title “Capacity Loaded Transmission Line for Subpicosecond Stepped Δβ Operation of an Integrated Optical Directional Coupler Switch”.
The active segments are separated by passive segments, in which the optical field is unaffected by the applied control voltage. The electrical transmission line is here implemented as loaded transmission line comprising a passive electrical transmission line implemented as an asymmetric co-planar line on the side of the optical waveguides, which are connected to several modulator segments, see FIGS. 1 and 2. The characteristic impedance of the co-planar line and the length of the modulator segments are adjusted to meet the requirements of velocity matching and preferred device impedance (usually 50Ω) according to design rules outlined in the article by Walker, see below.
FIG. 1 shows a schematic of travelling wave Mach-Zehnder modulator 10 using a capacitively loaded co-planar passive microwave transmission line 11 and three-guide coupler split/recombine regions. The passive microwave transmission line (TML) 11, having the characteristic impedance Zp and propagation index np:
                                          Z            p                    =                                                    L                p                                            C                p                                                    ,                              and            ⁢                                                  ⁢                          n              p                                =                                    c              0                        ⁢                                                            L                  p                                ⁢                                  C                  p                                                                    ,                            (        1        )            where Lp and Cp is the inductance and capacitance per unit length of the TML, respectively. The passive waveguide is capacitively loaded by a number of modulator sections 12 each with a length lm, a (centre to centre) spacing ls, and a capacitance per unit length Cm. The device 10 further includes optical couplers, RF source and termination.
FIGS. 2a and 2b show cross-sectional views along A-A and B-B, respectively, in FIG. 1. FIG. 2a shows a cross-section of a passive section of the modulator according to Walker's design having two adjacent optical waveguides WG arranged on a substrate Sub, with a ground plane 13 arranged on one side of the waveguides WG and a transmission line TML arranged on the other side of the waveguides. FIG. 2b shows a cross-section of an active section of the of the modulator according to Walker's design having the same features as the passive section and an additional conductive bridge 14 between the transmission line 11, alternatively the ground plane 13, and each modulator section 12.
The resulting effective (Bloch) impedance and propagation index is then expressed as:
                                          Z            B                    =                                                    L                p                                                              C                  p                                +                                                      C                    m                                    ⁢                                                            l                      m                                                              l                      s                                                                                                          ,                              and            ⁢                                                  ⁢                          n              B                                =                                    c              0                        ⁢                                                            L                  p                                ⁡                                  (                                                            C                      p                                        +                                                                  C                        m                                            ⁢                                                                        l                          m                                                                          l                          s                                                                                                      )                                                                    ,                            (        2        )            
The optical and electrical velocity is matched (nB=n0) if (according to Walker):
                                          C            m                    ⁢                                    l              m                                      l              s                                      =                                                            n                0                2                            -                              n                p                2                                                                    c                0                2                            ⁢                              L                p                                              =                                                                      n                  0                  2                                -                                  n                  p                  2                                                                              c                  0                                ⁢                                  Z                  p                                ⁢                                  n                  p                                                      .                                              (        3        )            
Resulting in an effective (Bloch) impedance of:
                              Z          B                =                                            Z              p                        ⁢                                          n                p                                            n                B                                              =                                    Z              p                        ⁢                                                                                ɛ                    eff                                                                    n                  B                                            .                                                          (        4        )            
An alternative expression for (3) is then given as:
                                          C            m                    ⁢                                    l              m                                      l              s                                      =                                                            n                B                2                            -                              n                p                2                                                                    c                0                2                            ⁢                              L                p                                              =                                                    n                B                2                            -                              n                p                2                                                                    c                0                            ⁢                              Z                B                            ⁢                              n                B                                                                        (        5        )            